To obtain an approximated value of sqrt(a), one can use Newton's method:
with a given real x. This can be easily implemented in computer programs such as MATLAB or SCILAB, but today I will represent this as a feedback system.
First, the iteration can be represented by
where σ denotes the shift operator
In control theory or signal processing, this operator is also denoted by z-1. Next, the iteration is divided into two parts, φ and σ, that is,
Finally, this can be represented by the following block diagram:
This is a "feedback system" for sqrt(2). You can change the initial value x by double-clicking "1/z" block. Also, if you want another square root, double-click the "Expression" block and change "2" in the numerator to another positive number. But, if you feel like wilding out, use a negative number instead. In this case, the sequence will not converge, but show some chaotic behavior. The following is the result for "-2."